Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 2142, 1524 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 2142, 1524 is 6 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 2142, 1524 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 2142, 1524 is 6.
HCF(2142, 1524) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2142, 1524 is 6.
Step 1: Since 2142 > 1524, we apply the division lemma to 2142 and 1524, to get
2142 = 1524 x 1 + 618
Step 2: Since the reminder 1524 ≠ 0, we apply division lemma to 618 and 1524, to get
1524 = 618 x 2 + 288
Step 3: We consider the new divisor 618 and the new remainder 288, and apply the division lemma to get
618 = 288 x 2 + 42
We consider the new divisor 288 and the new remainder 42,and apply the division lemma to get
288 = 42 x 6 + 36
We consider the new divisor 42 and the new remainder 36,and apply the division lemma to get
42 = 36 x 1 + 6
We consider the new divisor 36 and the new remainder 6,and apply the division lemma to get
36 = 6 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 2142 and 1524 is 6
Notice that 6 = HCF(36,6) = HCF(42,36) = HCF(288,42) = HCF(618,288) = HCF(1524,618) = HCF(2142,1524) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 2142, 1524?
Answer: HCF of 2142, 1524 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2142, 1524 using Euclid's Algorithm?
Answer: For arbitrary numbers 2142, 1524 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.